VOL. LXXXVIII.] PHILOSOPHICAL TRANSACTIONS. 355 



Corol. 4. In order to describe this curve from its equation ; change the one given 

 above, by transferring the axes of its co-ordinates : it becomes (y being = p'm and 



x = ap'), ^-/((f-^ + rfxh. 1. d * _ j2) ; which may be used with 



ease, by changing the hyperbolic into the tabular logarithm. Thus then, the com- 

 mon logarithmic has its subtangent constant ; the conic parabola, its subnormal ; 

 the circle, its normal ; and the curve which I have described in this proposition, 

 its tangent. 



XVIII. Observations of the Diurnal Variation of the Magnetic Needle, in the 

 Island of St. Helena ; with a Continuation of the Observations at Fort Marlbo- 

 rough, in the Island of Sumatra. By John Macdonald, Esq. p. 397. 



A short residence at St. Helena, arising from the sudden departure of the fleet 

 to which the ship I was in belonged, has prevented the observations from being so 

 numerous as I could wish. Their agreement however indicates that 58 observations 

 are sufficient for affording such conclusions as philosophy may draw ; and tends to 

 confirm some inferences stated in a former paper, containing similar observations 

 taken in the East Indies. By adding the mean of the morning and afternoon ob- 

 servations, at St. Helena, and taking the half, the general variation, in the month 

 of November, 179^, appears to have been 15° 48' 344- // west: and by subtracting 

 the medium diurnal afternoon variation, from the medium diurnal morning, 

 the vibrating variation proves to be 3' bb" . It appears that the magnetic 

 needle is stationary from about 6 o'clock ■ in the evening till 6 in the morn- 

 ing ; when it commences moving, and the west variation increases, till it amounts 

 to its maximum, about 8 o'clock ; diminishing afterwards till it becomes sta- 

 tionary. Here the same cause seems to operate as at Bencoolen, with a modi- 

 fication of effect proportioned to the relative situation of the southern mag- 

 netic poles, and the places of observation. At the apartments of the k. s., this 

 species of variation is found to increase, from 7 o'clock in the morning till 2 in the 

 afternoon. If the variation is east, in the northern hemisphere in the East Indies, 

 I conceive that the diurnal variation will increase towards the afternoon, remain 

 some time stationary, and diminish before the succeeding morning : if the general 

 variation is west in that quarter, the reverse may be the case. The quantity of the 

 diurnal variation is greater in Britain than at St. Helena, or at Bencoolen. This 

 will naturally arise from this country's being more contiguous to its affecting poles, 

 than those islands, situated near the equator. It were to be wished, that obser- 

 vations were taken in as many situations as possible, similarly situated in the oppo- 

 site hemispheres, on the lines of no variation. A greater degree of dip might be 

 found, and conclusions might be deduced, that would tend considerably to illustrate 

 this curious and interesting subject, as yet involved in conjecture and uncertainty. 

 I frequently, while at Bencoolen, observed that the needle did not retain the same 

 level, but was sometimes depressed, and sometimes elevated, 6 or 8 minutes. I 

 paid little attention to this, ascribing it to a minute alteration in the position of 



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